Sorafenib and Erlotinib in Treating Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer That Has Not Responded to Chemotherapy

DISEASE CHARACTERISTICS: * Histologically or cytologically confirmed non-small cell lung cancer * Advanced (stage IIIB-IV) or recurrent disease * Must have failed 1 or 2 prior chemotherapy regimens, including platinum-containing regimen * At least 1 unidimensionally measurable lesion \> 10 mm by spiral CT scan or \> 20 mm by conventional CT scan * Previously irradiated lesions cannot be included as sites of measurable disease unless clear tumor progression has been documented in the lesions since the end of radiotherapy * No known or suspected brain metastases * Patients with clinical signs or symptoms that are suspicious of brain metastasis must have a pre-treatment CT scan or MRI of the brain * Patients with prior brain metastases are eligible provided they have completed their treatment for brain metastases, no longer require corticosteroids, and are asymptomatic PATIENT CHARACTERISTICS: * ECOG performance status 0-2 * WBC 4,000-12,000/μL * Neutrophil ≥ 1,500/μL * Platelet count ≥ 100,000/μL * Hemoglobin ≥ 9.0 g/dL * Total bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST and ALT ≤ 2.0 times ULN * Alkaline phosphatase ≤ 2.0 times ULN * Serum creatinine ≤ 1.5 times ULN * Not pregnant or nursing * No active clinically serious infections * No prior or concurrent cancer that is distinct in primary site or histology from the cancer being evaluated in this study except cervical carcinoma in situ, treated basal cell carcinoma, superficial bladder tumors (Ta, Tis and T1), or any cancer curatively treated \> 5 years before study * Able to swallow oral medications * No substance abuse or medical, psychological, or social conditions that may interfere with participation in the study or evaluation of the study results PRIOR CONCURRENT THERAPY: * See Disease Characteristics * Recovered from all prior therapy * No prior anti-EGFR targeted therapy * At least 4 weeks since prior surgery * At least 4 weeks since prior and no concurrent radiotherapy * No prior radiotherapy to the whole pelvis or chest or to ≥ 25% of the bone marrow * No other concurrent anticancer agents (e.g., chemotherapy or immunotherapy agents) which might affect evaluation of study treatment